For X-ray imaging, two effects which occur when X-rays pass through matter are usually considered, namely the absorption of a particular component of the X-rays and the phase shift of the transmitted X-rays.
In respect of the refractive index, which is given for X-rays byn=1−δ−iβ,  (1)the absorption depends on the size of the imaginary decrement β, which is related to the mass absorption coefficient μ/ρ byμ/ρ=4πβ/λ,  (2)where λ is the wavelength, μ is the linear absorption coefficient and ρ is the mass density.
The phase shift follows from the real part of the refractive index 1−δ. The phase shift Δ of an X-ray wave in matter compared to a vacuum is given byΔ=2πδT/λ,  (3)where T is the thickness of the material and δ is the real decrement of the refractive index.
In X-radiography, the subject is exposed to X-rays and the transmitted intensity is recorded behind the object. With the aid of this measurement, projection images can be produced which show the absorption caused by the object. In X-ray tomography, more than one projection image is used in order to calculate a three-dimensional data set, which shows the spatial distribution of the absorption coefficients μ.
For phase contrast radiography and phase contrast tomography, it is necessary to evaluate the phase shift caused by the object. Similarly as absorption imaging, a three-dimensional data set can be calculated which shows the spatial distribution of the real part of the refractive index 1−δ.
Since the phase of a wave cannot be measured directly, the phase shift is firstly converted into a measurable intensity by interference of the wave to be studied with a reference wave. The practical conduct of such measurements, both in relation to projective recordings and in relation to tomographic recordings, is presented by way of example in the European patent application EP 1 447 046 A1 and in the German patent applications with the file references 10 2006 017 290.6, 10 2006 015 358.8, 10 2006 017 291.4, 10 2006 015 356.1 and 10 2006 015 355.3 of the same priority.
The method presented there uses a phase grating placed in the beam path behind the subject, which acts as a diffraction grating and splits the X-rays into +1st and −1st order rays. In the wave field behind the phase grating, the diffracted rays interfere with one another to form an X-ray standing wave field. The subject causes local phase shifts, which deform the wavefront and therefore locally modify the amplitude, phase and offset of the standing wave field. By using a measurement which delivers information about the standing wave field, such as the phase, amplitude and average value of the standing waves, it is therefore possible to calculate the influence of the local phase shifts due to the subject. In order to scan the wave field with the requisite resolution, an analyzer grating is displaced stepwise over the wave field while the intensity is synchronously monitored pixel-wise by using a corresponding detector.
In the European patent application EP 1 447 046 A1 cited above, parallel X-rays are used for scanning the subject. Considered superficially, it could be assumed that an arbitrary magnification effect would be achievable by using divergent radiation geometries and correspondingly positioning the subject in the beam path. But when considering the effect of the radiation being refracted by the subject, it is found that measurement of the phase shift no longer appears possible because it is to be expected that a “chaotic” pattern of the deviated rays will occur, which does not lead to an evaluatable image rendition. For this reason, no X-ray phase contrast measurements have actually been carried out in a magnifying geometry by using phase gratings.